Interplay between two phase flow and rock mechanics: Exploring the rheology of melt-rock mixtures

地球的韧性地壳的很大一部分是由熔融岩石混合物组成的。这些两相物质在地壳的流变行为中起着重要作用，对地震周期和地震灾害具有重要意义。在熔融岩石混合物中，熔融物可以被“挤出”、“流过”或“积聚在”地壳中。该项目的目的是确定每种情况下的典型模式，并确定其流变后果。学生将从应用数学的角度评估两相流，重点是在与地球地壳和地幔相关的条件下使用数学模型的两相流的流变后果，并将新兴模式与岩石记录中看到的模式进行比较。学生将建立一个数学框架，以建立上述三种场景的流变响应，特别关注场景参数场和流变学在时间和空间上的动态变化。数值和数学的结果将分析不仅在流变学方面，而且在图案的形成。确定不同模式出现的条件将有助于与自然记录中观察到的地质特征进行直接比较。地质数据将从特定的地质环境（例如苏格兰、北方意大利）以及现有的报告结构中收集。

A significant portion of the Earth's ductile crust constitutes melt-rock mixtures. These two-phase materials play a major role in the rheological behaviour of the Earth's crust, with important implications for earthquakes cycles and seismic hazards. Within the melt-rock mixtures melt can be "squeezed out", "fluxed through", or "accumulated within" the Earth's crust. The aim of the project is to identify patterns typical for each scenario and establish their rheological consequences. The student will assess two-phase flow from an applied mathematical perspective, focussing on the rheological consequences of two phase flow using mathematical models at conditions relevant to the Earths' crust and mantle and comparing emerging patterns to those seen in the rock record. The student will establish a mathematical framework to establish the rheological response of the three scenarios described above with special focus on the dynamic changes in scenario parameter fields and rheology through time and space. Numerical and mathematical results will be analysed not only in terms of rheology but also in terms of pattern formation. Identification of the conditions for different patterns to arise will allow direct comparison to geological features observed in the natural record. Geological data will be collected from specific geological environments (e.g. Scotland, Northern Italy) as well as from existing reported structures.